Dimensional Reduction Near the Deconfinement Transition

When ordinary nuclear matter is heated to a high temperature of ~ 10^12 K, it undergoes a deconfinement transition to a new phase, strongly interacting quark-gluon plasma. While the color charged fundamental constituents of the nuclei, the quarks and gluons, are at low temperatures permanently confined inside color neutral hadrons, in the plasma the color degrees of freedom become dominant over nuclear, rather than merely nucleonic, volumes. Quantum Chromodynamics (QCD) is the accepted theory of the strong interactions, and confines quarks and gluons inside hadrons. The theory was formulated in early seventies, but deriving first principles predictions from it still remains a challenge, and novel methods of studying it are needed. One such method is dimensional reduction, in which the high temperature dynamics of static observables of the full four-dimensional theory are described using a simpler three-dimensional effective theory, having only the static modes of the various fields as its degrees of freedom. A perturbatively constructed effective theory is known to provide a good description of the plasma at high temperatures, where asymptotic freedom makes the gauge coupling small. In addition to this, numerical lattice simulations have, however, shown that the perturbatively constructed theory gives a surprisingly good description of the plasma all the way down to temperatures a few times the transition temperature. Near the critical temperature, the effective theory, however, ceases to give a valid description of the physics, since it fails to respect the approximate center symmetry of the full theory. The symmetry plays a key role in the dynamics near the phase transition, and thus one expects that the regime of validity of the dimensionally reduced theories can be significantly extended towards the deconfinement transition by incorporating the center symmetry in them. In the introductory part of the thesis, the status of dimensionally reduced effective theories of high temperature QCD is reviewed, placing emphasis on the phase structure of the theories. In the first research paper included in the thesis, the non-perturbative input required in computing the g^6 term in the weak coupling expansion of the pressure of QCD is computed in the effective theory framework at an arbitrary number of colors. The two last papers on the other hand focus on the construction of the center-symmetric effective theories, and subsequently the first non-perturbative studies of these theories are presented. Non-perturbative lattice simulations of a center-symmetric effective theory for SU(2) Yang-Mills theory show --- in sharp contrast to the perturbative setup --- that the effective theory accommodates a phase transition in the correct universality class of the full theory. This transition is seen to take place at a value of the effective theory coupling constant that is consistent with the full theory coupling at the critical temperature.

Applications of dimensional reduction to electroweak and QCD matter

When heated to high temperatures, the behavior of matter changes dramatically. The standard model fields go through phase transitions, where the strongly interacting quarks and gluons are liberated from their confinement to hadrons, and the Higgs field condensate melts, restoring the electroweak symmetry. The theoretical framework for describing matter at these extreme conditions is thermal field theory, combining relativistic field theory and quantum statistical mechanics. For static observables the physics is simplified at very high temperatures, and an effective three-dimensional theory can be used instead of the full four-dimensional one via a method called dimensional reduction. In this thesis dimensional reduction is applied to two distinct problems, the pressure of electroweak theory and the screening masses of mesonic operators in quantum chromodynamics (QCD). The introductory part contains a brief review of finite-temperature field theory, dimensional reduction and the central results, while the details of the computations are contained in the original research papers. The electroweak pressure is shown to converge well to a value slightly below the ideal gas result, whereas the pressure of the full standard model is dominated by the QCD pressure with worse convergence properties. For the mesonic screening masses a small positive perturbative correction is found, and the interpretation of dimensional reduction on the fermionic sector is discussed.

The effects of the 2004 reduction in the price of alcohol on alcohol-related harm in Finland : A natural experiment based on register data

Changes in alcohol pricing have been documented as inversely associated with changes in consumption and alcohol-related problems. Evidence of the association between price changes and health problems is nevertheless patchy and is based to a large extent on cross-sectional state-level data, or time series of such cross-sectional analyses. Natural experimental studies have been called for. There was a substantial reduction in the price of alcohol in Finland in 2004 due to a reduction in alcohol taxes of one third, on average, and the abolition of duty-free allowances for travellers from the EU. These changes in the Finnish alcohol policy could be considered a natural experiment, which offered a good opportunity to study what happens with regard to alcohol-related problems when prices go down. The present study investigated the effects of this reduction in alcohol prices on (1) alcohol-related and all-cause mortality, and mortality due to cardiovascular diseases, (2) alcohol-related morbidity in terms of hospitalisation, (3) socioeconomic differentials in alcohol-related mortality, and (4) small-area differences in interpersonal violence in the Helsinki Metropolitan area. Differential trends in alcohol-related mortality prior to the price reduction were also analysed. A variety of population-based register data was used in the study. Time-series intervention analysis modelling was applied to monthly aggregations of deaths and hospitalisation for the period 1996-2006. These and other mortality analyses were carried out for men and women aged 15 years and over. Socioeconomic differentials in alcohol-related mortality were assessed on a before/after basis, mortality being followed up in 2001-2003 (before the price reduction) and 2004-2005 (after). Alcohol-related mortality was defined in all the studies on mortality on the basis of information on both underlying and contributory causes of death. Hospitalisation related to alcohol meant that there was a reference to alcohol in the primary diagnosis. Data on interpersonal violence was gathered from 86 administrative small-areas in the Helsinki Metropolitan area and was also assessed on a before/after basis followed up in 2002-2003 and 2004-2005. The statistical methods employed to analyse these data sets included time-series analysis, and Poisson and linear regression. The results of the study indicate that alcohol-related deaths increased substantially among men aged 40-69 years and among women aged 50-69 after the price reduction when trends and seasonal variation were taken into account. The increase was mainly attributable to chronic causes, particularly liver diseases. Mortality due to cardiovascular diseases and all-cause mortality, on the other hand, decreased considerably among the-over-69-year-olds. The increase in alcohol-related mortality in absolute terms among the 30-59-year-olds was largest among the unemployed and early-age pensioners, and those with a low level of education, social class or income. The relative differences in change between the education and social class subgroups were small. The employed and those under the age of 35 did not suffer from increased alcohol-related mortality in the two years following the price reduction. The gap between the age and education groups, which was substantial in the 1980s, thus further broadened. With regard to alcohol-related hospitalisation, there was an increase in both chronic and acute causes among men under the age of 70, and among women in the 50-69-year age group when trends and seasonal variation were taken into account. Alcohol dependence and other alcohol-related mental and behavioural disorders were the largest category in both the total number of chronic hospitalisation and in the increase. There was no increase in the rate of interpersonal violence in the Helsinki Metropolitan area, and even a decrease in domestic violence. There was a significant relationship between the measures of social disadvantage on the area level and interpersonal violence, although the differences in the effects of the price reduction between the different areas were small. The findings of the present study suggest that that a reduction in alcohol prices may lead to a substantial increase in alcohol-related mortality and morbidity. However, large population group differences were observed regarding responsiveness to the price changes. In particular, the less privileged, such as the unemployed, were most sensitive. In contrast, at least in the Finnish context, the younger generations and the employed do not appear to be adversely affected, and those in the older age groups may even benefit from cheaper alcohol in terms of decreased rates of CVD mortality. The results also suggest that reductions in alcohol prices do not necessarily affect interpersonal violence. The population group differences in the effects of the price changes on alcohol-related harm should be acknowledged, and therefore the policy actions should focus on the population subgroups that are primarily responsive to the price reduction.

Training for reduction of design waste

Construction and demolition (C&D) waste have negative impacts on the environment. As a significant proportion of C&D waste is related to the design stage of a project, there is an opportunity for architects to reduce the waste. However, research suggests that many architects often do not understand the impact of their design on waste generation. Training and education are proposed by current researchers to improve architects’ knowledge; however, this has not been adequately validated as a viable approach to solving waste issues. This research investigates architects’ perceptions towards waste management in the design phase, and determines whether they feel they are adequately skilled in reducing C&D waste. Questionnaire surveys were distributed to architects from 98 architectural firms and 25 completed surveys were returned. The results show that while architects are aware of the relationship between design and waste, ‘extra time’ and ‘lack of knowledge’ are the key barriers to implementing waste reduction strategies. In addition, the majority of respondents acknowledge their lack of skill to reduce waste through design evaluation. Therefore, training programmes can be a viable strategy to enable them to address the pressing issue of C&D waste reduction.

Medicalising Prohibition : Harm reduction in Finnish and International Drug Policy

The increase in drug use and related harms in the late 1990s in Finland has come to be referred to as the second drug wave. In addition to using criminal justice as a basis of drug policy, new kinds of drug regulation were introduced. Some of the new regulation strategies were referred to as "harm reduction". The most widely known practices of harm reduction include needle and syringe exchange programmes for intravenous drug users and medicinal substitution and maintenance treatment programmes for opiate users. The purpose of the study is to examine the change of drug policy in Finland and particularly the political struggle surrounding harm reduction in the context of this change. The aim is, first, to analyse the content of harm reduction policy and the dynamics of its emergence and, second, to assess to what extent harm reduction undermines or threatens traditional drug policy. The concept of harm reduction is typically associated with a drug policy strategy that employs the public health approach and where the principal focus of regulation is on drug-related health harms and risks. On the other hand, harm reduction policy has also been given other interpretations, relating, in particular, to human rights and social equality. In Finland, harm reduction can also be seen to have its roots in criminal policy. The general conclusion of the study is that rather than posing a threat to a prohibitionist drug policy, harm reduction has come to form part of it. The implementation of harm reduction by setting up health counselling centres for drug users with the main focus on needle exchange and by extending substitution treatment has implied the creation of specialised services based on medical expertise and an increasing involvement of the medical profession in addressing drug problems. At the same time the criminal justice control of drug use has been intensified. Accordingly, harm reduction has not entailed a shift to a more liberal drug policy nor has it undermined the traditional policy with its emphasis on total drug prohibition. Instead, harm reduction in combination with a prohibitionist penal policy constitutes a new dual-track drug policy paradigm. The study draws on the constructionist tradition of research on social problems and movements, where the analysis centres on claims made about social problems, claim-makers, ways of making claims and related social mobilisation. The research material mainly consists of administrative documents and interviews with key stakeholders. The doctoral study consists of five original articles and a summary article. The first article gives an overview of the strained process of change of drug policy and policy trends around the turn of the millennium. The second article focuses on the concept of harm reduction and the international organisations and groupings involved in defining it. The third article describes the process that in 1996 97 led to the creation of the first Finnish national drug policy strategy by reconciling mutually contradictory views of addressing the drug problem, at the same as the way was paved for harm reduction measures. The fourth article seeks to explain the relatively rapid diffusion of needle exchange programmes after 1996. The fifth article assesses substitution treatment as a harm reduction measure from the viewpoint of the associations of opioid users and their family members.

Tradeoff between PAPR reduction and decoding complexity in transformed OFDM systems

It is known that in an OFDM system using Hadamard transform or phase alteration before the IDFT operation can reduce the Peak-to-Average Power Ratio (PAPR). Both these techniques can be viewed as constellation precoding for PAPR reduction. In general, using non-diagonal transforms, like Hadamard transform, increases the ML decoding complexity. In this paper we propose the use of block-IDFT matrices and show that appropriate block-IDFT matrices give lower PAPR as well as lower decoding complexity compared to using Hadamard transform. Moreover, we present a detailed study of the tradeoff between PAPR reduction and the ML decoding complexity when using block-IDFT matrices with various sizes of the blocks.

Formation of an oxo-radical of peroxovanadate during reduction of diperoxovanadate with vanadyl sulfate or ferrous sulfate

Formation of oxygen radicals during reduction of H2O2 or diperoxovanadate with vanadyl sulfate or ferrous sulfate was indicated by the 1:2:2:1 electron spin resonance (ESR) signals of the DMPO adduct typical of standard radical dotOH radical. Signals derived from diperoxovanadate remained unchanged in the presence of ethanol in contrast to those from H2O2. This gave the clue that they represent a different radical, possibly radical dotOV(O2)2+, formed on breaking a peroxo-bridge of diperoxovanadate complex. The above reaction mixtures evolved dioxygen or, when NADH was present, oxidized it rapidly which was accompanied by consumption of dioxygen. Operation of a cycle of peroxovanadates including this new radical is suggested to explain these redox activities both with vanadyl and ferrous sulfates. It can be triggered by ferrous ions released from cellular stores in the presence of catalytic amounts of peroxovanadates.

Humanitaarisuuden varjossa : Poliittiset tekijät lastensiirroissa Ruotsiin sotiemme aikana ja niiden jälkeen

The evacuation of Finnish children to Sweden during WW II has often been called a small migration . Historical research on this subject is scarce, considering the great number of children involved. The present research has applied, apart from the traditional archive research, the framework of history-culture developed by Rüsen in order to have an all-inclusive approach to the impact of this historical event. The framework has three dimensions: political, aesthetic and cognitive. The collective memory of war children has also been discussed. The research looks for political factors involved in the evacuations during the Winter War and the Continuation War and the post-war period. The approach is wider than a purely humanitarian one. Political factors have had an impact in both Finland and Sweden, beginning from the decision-making process and ending with the discussion of the unexpected consequences of the evacuations in the Finnish Parliament in 1950. The Winter War (30.11.1939 13.3.1940) witnessed the first child transports. These were also the model for future decision making. The transports were begun on the initiative of Swedes Maja Sandler, the wife of the resigned minister of foreign affairs Rickard Sandler, and Hanna Rydh-Munck af Rosenschöld , but this activity was soon accepted by the Swedish government because the humanitarian help in the form of child transports lightened the political burden of Prime Minister Hansson, who was not willing to help Finland militarily. It was help that Finland never asked for and it was rejected at the beginning. The negative response of Minister Juho Koivisto was not taken very seriously. The political forces in Finland supporting child transports were stronger than those rejecting them. The major politicians in support belonged to Finland´s Swedish minority. In addition, close to 1 000 Finnish children remained in Sweden after the Winter War. No analysis was made of the reasons why these children did not return home. A committee set up to help Finland and Norway was established in Sweden in 1941. Its chairman was Torsten Nothin, an influential Swedish politician. In December 1941 he appealed to the Swedish government to provide help to Finnish children under the authority of The International Red Cross. This plea had no results. The delivery of great amounts of food to Finland, which was now at war with Great Britain, had automatically caused reactions among the allies against the Swedish imports through Gothenburg. This included the import of oil, which was essential for the Swedish navy and air force. Oil was later used successfully to force a reduction in commerce between Sweden and Finland. The contradiction between Sweden´s essential political interests and humanitarian help was solved in a way that did not harm the country´s vital political interests. Instead of delivering help to Finland, Finnish children were transported to Sweden through the organisations that had already been created. At the beginning of the Continuation War (25.6.1941 27.4.1945) negative opinion regarding child transports re-emerged in Finland. Karl-August Fagerholm implemented the transports in September 1941. In 1942, members of the conservative parties in the Finnish Parliament expressed their fear of losing the children to the Swedes. They suggested that Finland should withdraw from the inter-Nordic agreement, according to which the adoptions were approved by the court of the country where the child resided. This initiative failed. Paavo Virkkunen, an influential member of the conservative party Kokoomus in Finland, favoured the so-called good-father system, where help was delivered to Finland in the form of money and goods. Virkkunen was concerned about the consequences of a long stay in a Swedish family. The risk of losing the children was clear. The extreme conservative party (IKL, the Patriotic Movement of the Finnish People) wanted to alienate Finland from Sweden and bring Finland closer to Germany. Von Blücher, the German ambassador to Finland, had in his report to Berlin, mentioned the political consequences of the child transports. Among other things, they would bring Finland and Sweden closer to each other. He had also paid attention to the Nordic political orientation in Finland. He did not question or criticize the child transports. His main interest was to increase German political influence in Finland, and the Nordic political orientation was an obstacle. Fagerholm was politically ill-favoured by the Germans, because he had a strong Nordic political disposition and had criticised Germany´s activities in Norway. The criticism of child transports was at the same time criticism of Fagerholm. The official censorship organ of the Finnish government (VTL) denied the criticism of child transports in January 1942. The reasons were political. Statements made by members of the Finnish Parliament were also censored, because it was thought that they would offend the Swedes. In addition, the censorship organ used child transports as a means of active propaganda aimed at improving the relations between the two countries. The Finnish Parliament was informed in 1948 that about 15 000 Finnish children still remained in Sweden. These children would stay there permanently. In 1950 the members of the Agrarian Party in Finland stated that Finland should actively strive to get the children back. The party on the left (SKDL, the Democratic Movement of Finnish People) also focused on the unexpected consequences of the child transports. The Social Democrats, and largely Fagerholm, had been the main force in Finland behind the child transports. Members of the SKDL, controlled by Finland´s Communist Party, stated that the war time authorities were responsible for this war loss. Many of the Finnish parents could not get their children back despite repeated requests. The discussion of the problem became political, for example von Born, a member of the Swedish minority party RKP, related this problem to foreign policy by stating that the request to repatriate the Finnish children would have negative political consequences for the relations between Finland and Sweden. He emphasized expressing feelings of gratitude to the Swedes. After the war a new foreign policy was established by Prime Minister (1944 1946) and later President (1946 1956) Juho Kusti Paasikivi. The main cornerstone of this policy was to establish good relations with the Soviet Union. The other, often forgotten, cornerstone was to simultaneously establish good relations with other Nordic countries, especially Sweden, as a counterbalance. The unexpected results of the child evacuation, a Swedish initiative, had violated the good relations with Sweden. The motives of the Democratic Movement of Finnish People were much the same as those of the Patriotic Movement of Finnish People. Only the ideology was different. The Nordic political orientation was an obstacle to both parties. The position of the Democratic Movement of Finnish People was much better than that of the Patriotic Movement of Finnish People, because now one could clearly see the unexpected results, which included human tragedy for the many families who could not be re-united with their children despite their repeated requests. The Swedes questioned the figure given to the Finnish Parliament regarding the number of children permanently remaining in Sweden. This research agrees with the Swedes. In a calculation based on Swedish population registers, the number of these children is about 7 100. The reliability of this figure is increased by the fact that the child allowance programme began in Sweden in 1948. The prerequisite to have this allowance was that the child be in the Swedish population register. It was not necessary for the child to have Swedish nationality. The Finnish Parliament had false information about the number of Finnish children who remained in Sweden in 1942 and in 1950. There was no parliamentary control in Finland regarding child transports, because the decision was made by one cabinet member and speeches by MPs in the Finnish Parliament were censored, like all criticism regarding child transports to Sweden. In Great Britain parliamentary control worked better throughout the whole war, because the speeches regarding evacuation were not censored. At the beginning of the war certain members of the British Labour Party and the Welsh Nationalists were particularly outspoken about the scheme. Fagerholm does not discuss to any great extent the child transports in his memoirs. He does not evaluate the process and results as a whole. This research provides some possibilities for an evaluation of this sort. The Swedish medical reports give a clear picture of the physical condition of the Finnish children when arriving in Sweden. The transports actually revealed how bad the situation of the poorest children was. According to Titmuss, similar observations were made in Great Britain during the British evacuations. The child transports saved the lives of approximately 2 900 children. Most of these children were removed to Sweden to receive treatment for illnesses, but many among the healthy children were undernourished and some suffered from the effects of tuberculosis. The medical inspection in Finland was not thorough. If you compare the figure of 2 900 children saved and returned with the figure of about 7 100 children who remained permanently in Sweden, you may draw the conclusion that Finland as a country failed to benefit from the child transports, and that the whole operation was a political mistake with far-reaching consequenses. The basic goal of the operation was to save lives and have all the children return to Finland after the war. The difficulties with the repatriation of the children were mainly psychological. The level of child psychology in Finland at that time was low. One may question the report by Professor Martti Kaila regarding the adaptation of children to their families back in Finland. Anna Freud´s warnings concerning the difficulties that arise when child evacuees return are also valid in Finland. Freud viewed the emotional life of children in a way different from Kaila: the physical survival of a small child forces her to create strong emotional ties to the person who is looking after her. This, a characteristic of all small children, occurred with the Finnish children too, and it was something the political decision makers in Finland could not see during and after the war. It is a characteristic of all little children. Yet, such experiences were already evident during the Winter War. The best possible solution had been to limit the child transports only to children in need of medical treatment. Children from large and poor families had been helped by organising meals and by buying food from Denmark with Swedish money. Assisting Finland by all possible means should have been the basic goal of Fagerholm in September 1941, when the offer of child transports came from Sweden. Fagerholm felt gratitude towards the Swedes. The risks became clear to him only in 1943. The war children are today a rather scattered and diffuse group of people. Emotionally, part of these children remained in Sweden after the war. There is no clear collective memory, only individual memories; the collective memory of the war children has partly been shaped later through the activities of the war child associations. The main difference between the children evacuated in Finland (for example from Karelia to safer areas with their families) and the war children, who were sent abroad, is that the war children lack a shared story and experience with their families. They were outsiders . The whole matter is sensitive to many of such mothers and discussing the subject has often been avoided in families. The war-time censorship has continued in families through silence and avoidance and Finnish politicians and Finnish families had to face each other on this issue after the war. The lack of all-inclusive historical research has also prevented the formation of a collective awareness among war children returned to Finland or those remaining permanently abroad.. Knowledge of historical facts will help war-children by providing an opportunity to create an all-inclusive approach to the past. Personal experiences should be regarded as part of a large historical entity shadowed by war and where many political factors were at work in both Finland and Sweden. This means strengthening of the cognitive dimension discussed in Rüsen´s all-inclusive historical approach.

Reactions with disulphur monoxide solutions obtained by the reduction of cupric oxide by elemental sulphur

When the products of reaction between elemental sulphur and copper oxide at elevated temperature in vacuum are bubbled through chilled inert organic solvents like carbontetrachloride, orange-yellow solutions were obtained indicating the presence of lower oxide of sulphur. This lower oxide has been found to be disulphur monoxide as shown by three different types of reactions; (1) Mercury decomposition, (2) Reaction with hydrogen iodide and hydrolytic reaction in an alkaline homogeneous medium.

Reduction of Torque Ripple in Induction Motor Drives Using an AdvancedHybrid PWM Technique

A voltage source inverter-fed induction motor produces a pulsating torque due to application of nonsinusoidal voltages. Torque pulsation is strongly influenced by the pulsewidth modulation (PWM) method employed. Conventional space vector PWM (CSVPWM) is known to result in less torque ripple than sine-triangle PWM. This paper aims at further reduction in the pulsating torque by employing advanced bus-clamping switching sequences, which apply an active vector twice in a subcycle. This paper proposes a hybrid PWM technique which employs such advanced bus-clamping sequences in conjunction with a conventional switching sequence. The proposed hybrid PWM technique is shown to reduce the torque ripple considerably over CSVPWM along with a marginal reduction in current ripple.

Steroids and related natural products. VII. Boron trifluoride etherate-lithium aluminum hydride reduction of smilagenin acetate

Reduction of smilagenin acetate (Va) using a boron trifluoride etherate-lithium aluminum hydride reagent, followed by hydrogen peroxide oxidation and acetylation, was found to yield: 3β-ethoxysmilagenin (Vb), 3β-ethoxydihydrosmilagenin acetate (VIa), dihydrosmilagenin diacetate (VIb), and a complex mixture of partially acetylated products. Similar reaction conditions were employed to convert dihydrodiosgenin (II) to dihydrochlorogenin (III). Boron trifluoride etherate-lithium aluminum hydride reduction of 3β-acetoxy-5α-cholestane and 3β-acetoxy-5α-lanostane (VIIIa) was shown to yield the corresponding 3β-ethoxy (e.g., VIIIb) derivatives.

Colorimetric determination of 2,4-dinitrophenylamino groups by sodium borohydride reduction

When sodium borohydride is added to aqueous solutions of 2,4-dinitrophenylamino acids and related derivatives, an intense red color is formed. Measurement of the red color, with a 420 filter, permits the determination of such compounds in concentrations of 0.01 to 0.06 μmole per ml. with a precision to 2%. The reaction is highly specific-while 2,4-dinitroaniline will react to the test, o-, m-, and p-nitroanilines, 2,4-dinitrophenyl aryl or alkyl ethers, and 2,4-dinitrophenyl-imidazole and pyrrolidine derivatives will not. Heretofore aromatic nitro groups have been considered resistant to attack by sodium borohydride. The method, as developed, is applicable to the evaluation of the degree of substitution of protein amino groups by fluorodinitrobenzene.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.